| DataSet | GRT low | GRT high | Distance Threshold | Proximity Criterion | Deers | Observations |
|---|---|---|---|---|---|---|
| 1 | 19 | 50 | 10 | last | 30 | 99 |
| 2 | 19 | 50 | 10 | nearest | 30 | 98 |
| 3 | 0 | 50 | 10 | score | 36 | 281 |
Modelling Fecal Cortisol Metabolites
Dr. Nicolas Ferry - Bavarian National Forest Park / Daniel Schlichting - StabLab
31 Jan 2025

model FCM levels on spatial and temporal distance to hunting activities
Expectation: FCM levels higher when closer in time and space
Note: The defecation location is not the deer’s location at the time of the stress event.
Movement: contains the location and datetime of the 41 collared deer in the period Feb 2020 - Feb 2023 in the Bavarian Forest National Park. Movement is tracked at hourly intervals.
Hunting Events: contains location and date of hunting events in the Bavarian Forest National Park - in total 1270 events, 890 of them with full timestamp.
FCM Stress: contains information of 809 faecal samples, including
Reproduction Success: contains information about of 16 collared deer about
TBD: Illustration.
We introduce 4 parameters:
A hunting event is considered relevant to an FCM sample, if
Among the relevant hunting events, the most relevant one is defined by the proximity criterion:
The scoring function is defined as TBD.
We suggest 3 different datasets for modelling
| DataSet | GRT low | GRT high | Distance Threshold | Proximity Criterion | Deers | Observations |
|---|---|---|---|---|---|---|
| 1 | 19 | 50 | 10 | last | 30 | 99 |
| 2 | 19 | 50 | 10 | nearest | 30 | 98 |
| 3 | 0 | 50 | 10 | score | 36 | 281 |
For Modelling, we consider the following covariates, defined for each pair of FCM sample and most relevant hunting event:
Generalized additive mixed model with Gamma family and log link.
Let \(i = 1,\dots,N\) be the indices of deer and \(j = 1,\dots,n_i\) be the indices of FCM measurements for each deer. \[ \begin{eqnarray} \textup{FCM}_{ij} &\sim& \mathcal{Ga}\left( \nu, \frac{\nu}{\mu_{ij}} \right) \\ \mu_{ij} &=& \mathbb{E}(\textup{FCM}_{ij}) = \exp(\eta_{ij}) \\ \eta_{ij} &=& \beta_0 + \beta_1 \textup{Pregnant}_{ij} + \beta_2 \textup{NumberOtherHunts}_{ij} + \\ && f_1(\textup{TimeDiff}_{ij}) + f_2(\textup{Distance}_{ij}) + \\ && f_3(\textup{SampleDelay}_{ij}) + f_4(\textup{DefecationDay}_{ij}) + \\ && \gamma_{i}, \\ \gamma_i &\sim& \mathcal{N}(0, \sigma_\gamma^2). \end{eqnarray} \]
\(f_1, \dots, f_4\) are penalized cubic regression splines.
| A. parametric coefficients | Estimate | Std. Error | t-value | p-value |
| (Intercept) | 5.6456 | 0.0692 | 81.5409 | < 0.0001 |
| PregnantTRUE | 0.1455 | 0.1277 | 1.1386 | 0.2583 |
| NumOtherHunts | 0.0204 | 0.1128 | 0.1809 | 0.8569 |
| B. smooth terms | edf | Ref.df | F-value | p-value |
| s(TimeDiff) | 1.0000 | 1.0000 | 0.0119 | 0.9133 |
| s(Distance) | 8.8584 | 8.9832 | 3.1531 | 0.0019 |
| s(SampleDelay) | 2.2208 | 2.7579 | 3.0379 | 0.0256 |
| s(DefecDay) | 5.9958 | 7.2374 | 1.5743 | 0.1540 |
| s(Deer.ID) | 0.0000 | 29.0000 | 0.0000 | 0.8489 |
Large uncertainty, no visible time or distance effect
Not many observations after datafusion left for robust modelling
Trade-off between spatial and temporal distance
Sample Delay seems to be significant
Modelling Outcomes don’t show much difference
Trade-off between Complexity and Explainability
How to minimize spatial and temporal distance at the same time?
How to use a bigger Part of the Data?
Effect of Hunting on Red Deer